Mathematics and computing articles within Nature Physics

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  • Article |

    The phrase ‘arrow of time’ refers to the asymmetry in the flow of events. A machine learning algorithm trained to infer its direction identifies entropy production as the relevant underlying physical principle in the decision-making process.

    • Alireza Seif
    • , Mohammad Hafezi
    •  & Christopher Jarzynski

  • Article |

    The authors investigate the relationship between the volume of malignant tumours and their metabolic processes using a large dataset of patients with cancer. They find that cancers follow a superlinear metabolic scaling law, which implies that the proliferation of cancer cells accelerates with increasing volume.

    • Víctor M. Pérez-García
    • , Gabriel F. Calvo
    •  & Ana M. García Vicente

  • News & Views |

    Near-term quantum computations are susceptible to noise that — left uncorrected — can destroy the correlations responsible for quantum computational speedups. New work develops tools for bolstering the noise resilience of these speedups.

    • Bill Fefferman

  • Comment |

    Automated learning from data by means of deep neural networks is finding use in an ever-increasing number of applications, yet key theoretical questions about how it works remain unanswered. A physics-based approach may help to bridge this gap.

    • Lenka Zdeborová

  • Perspective |

    This Perspective argues that an approach called extreme value theory is appropriate for understanding the so-called tail risk of epidemic outbreaks, in particular by demonstrating that the distribution of fatalities due to epidemic outbreaks over the past 2500 years is fat-tailed and dominated by extreme events.

    • Pasquale Cirillo
    •  & Nassim Nicholas Taleb

  • Comment |

    In 1985, experiments revealed the quantum behaviour of a macroscopic degree of freedom: the phase difference across a Josephson junction. The authors recount the history of this milestone for the development of superconducting quantum circuits.

    • John M. Martinis
    • , Michel H. Devoret
    •  & John Clarke

  • Letter |

    Knowledge of the spreading mechanisms of contagions is important for understanding a range of epidemiological and social problems. A study now shows that so-called simple and complex contagions cannot be told apart if there is more than one simple contagion traversing the population at the same time.

    • Laurent Hébert-Dufresne
    • , Samuel V. Scarpino
    •  & Jean-Gabriel Young

  • Perspective |

    This Perspective argues that ergodicity — a foundational concept in equilibrium statistical physics — is wrongly assumed in much of the quantitative economics literature. By asking the extent to which dynamical problems can be replaced by probabilistic ones, many economics puzzles are resolved in a natural and empirically testable fashion.

    • Ole Peters

  • News & Views |

    It is generally difficult to know in advance if a sheet of paper can be folded into an origami shape, but for quadrilateral crease patterns a tiling approach can identify all possible ways of folding them.

    • Christian Santangelo

  • Measure for Measure |

    From determining the compound interest on borrowed money to gauging chances at the roulette wheel in Monte Carlo, Stefanie Reichert explains that there’s no way around Euler’s number.

    • Stefanie Reichert

  • Article |

    A quantum circuit-based algorithm inspired by convolutional neural networks is shown to successfully perform quantum phase recognition and devise quantum error correcting codes when applied to arbitrary input quantum states.

    • Iris Cong
    • , Soonwon Choi
    •  & Mikhail D. Lukin

  • News & Views |

    A statistical analysis of data from ultra-relativistic heavy-ion collisions has uncovered the specific viscosities of the quark–gluon plasma — suggesting that the hottest matter in the current Universe behaves like a near-perfect fluid.

    • Kari J. Eskola

  • Article |

    Modelling and microscopy of thousands of cells together reveal the coupling through which the cell cycle influences the circadian clock. This coupling may explain why mammalian tissues growing at different rates have shifted circadian rhythms.

    • Colas Droin
    • , Eric R. Paquet
    •  & Felix Naef

  • Measure for Measure |

    Imaginary numbers have a chequered history, and a sparse — if devoted — following. Abigail Klopper looks at why a concept as beautiful as i gets such a bad rap.

    • Abigail Klopper

  • Letter |

    Quantum gas microscopes provide high-resolution real-space snapshots of quantum many-body systems. Now machine-learning techniques are used in choosing theoretical descriptions according to the consistency of their predictions with these snapshots.

    • Annabelle Bohrdt
    • , Christie S. Chiu
    •  & Michael Knap

  • News & Views |

    The mechanics of many materials can be modelled by a network of balls connected by springs. A bottom-up approach based on differential geometry now captures changes in mechanics upon network growth or merger, going beyond the linear deformation regime.

    • A. Souslov
    •  & V. Vitelli

  • Article |

    A bottom-up mathematical approach provides a framework for the design of mechanical networks of two- or three-dimensional frames composed of freely rotating rods and springs that achieve any desired coordinate motion.

    • Jason Z. Kim
    • , Zhixin Lu
    •  & Danielle S. Bassett

  • Perspective |

    Rich data are revealing that complex dependencies between the nodes of a network may not be captured by models based on pairwise interactions. Higher-order network models go beyond these limitations, offering new perspectives for understanding complex systems.

    • Renaud Lambiotte
    • , Martin Rosvall
    •  & Ingo Scholtes

  • Measure for Measure |

    In 2016, Peter Trueb computed 22.4 trillion digits of π. Ahead of π Day on 14 March, he reflects on the nature of π and its role in mathematics, science and philosophy.

    • Peter Trueb

  • Measure for Measure |

    Artificial intelligence is set to rival the human mind, just as the engine did the horse. José Hernández-Orallo looks at how we compare cognitive performance.

    • José Hernández-Orallo

  • Comment |

    Modern physics edged mechanics out into the wilds of engineering. But multidisciplinary interest in pattern formation has moved it back into the mainstream, bringing with it interest from other fields — as this summer’s Solvay Workshop demonstrated.

    • Pedro M. Reis
    • , Fabian Brau
    •  & Pascal Damman

  • Perspective |

    Despite the growing interdisciplinarity of research, the Nobel prize consolidates the traditional disciplinary categorization of science. There is, in fact, an opportunity for the most revered scientific reward to mirror the current research landscape.

    • Michael Szell
    • , Yifang Ma
    •  & Roberta Sinatra

  • Editorial |

    In praise of the Fields Medal.

  • Measure for Measure |

    Solid angle is an ancient notion with modern relevance. A one-page primer by Ben Kravitz.

    • Ben Kravitz

  • Letter |

    Knotted lines representing torus knot and figure-eight knot are produced in the polarization profile of optical beams, leading to a topological characterization of the structure of the polarization field.

    • Hugo Larocque
    • , Danica Sugic
    •  & Ebrahim Karimi

  • Comment |

    David Hilbert famously argued that infinity cannot exist in physical reality. The consequence of this statement — still under debate today — has far-reaching implications.

    • George F. R. Ellis
    • , Krzysztof A. Meissner
    •  & Hermann Nicolai

  • Letter |

    The organization of small clusters of connected cells confined to an egg chamber during early development can be mapped onto a tree packing problem. Entropically preferred packing configurations are shown to arise more readily in experiment.

    • Jasmin Imran Alsous
    • , Paul Villoutreix
    •  & Jörn Dunkel

  • Article |

    Finding the relevant degrees of freedom of a system is a key step in any renormalization group procedure. But this can be difficult, particularly in strongly interacting systems. A machine-learning algorithm proves adept at identifying them for us.

    • Maciej Koch-Janusz
    •  & Zohar Ringel

  • Article
    | Open Access

    Complex networks are not obviously renormalizable, as different length scales coexist. Embedding networks in a geometrical space allows the definition of a renormalization group that can be used to construct smaller-scale replicas of large networks.

    • Guillermo García-Pérez
    • , Marián Boguñá
    •  & M. Ángeles Serrano

  • Letter |

    A technique allows optimal inference of the structure of a network when the available observed data are rich but noisy, incomplete or otherwise unreliable.

    • M. E. J. Newman

  • News & Views |

    Quantum tomography infers quantum states from measurement data, but it becomes infeasible for large systems. Machine learning enables tomography of highly entangled many-body states and suggests a new powerful approach to this problem.

    • Pantita Palittapongarnpim
    •  & Barry C. Sanders

  • Letter |

    Unsupervised machine learning techniques can efficiently perform quantum state tomography of large, highly entangled states with high accuracy, and allow the reconstruction of many-body quantities from simple experimentally accessible measurements.

    • Giacomo Torlai
    • , Guglielmo Mazzola
    •  & Giuseppe Carleo

  • News & Views |

    Device-independent quantum cryptography promises unprecedented security, but it is regarded as a theorist's dream and an experimentalist's nightmare. A new mathematical tool has now pushed its experimental demonstration much closer to reality.

    • Artur Ekert

  • News & Views |

    A type of optics experiment called a boson sampler could be among the easiest routes to demonstrating the power of quantum computers. But recent work shows that super-classical boson sampling may be a long way off.

    • Andrew M. Childs

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